Kun Fang

Abstract The manipulation of quantum resources such as entanglement and coherence lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind of manipulation is to purify the quantum resources, since they are inevitably contaminated by noises and thus often lost their power or become unreliable for direct usage. In these two works, we establish a theory of the universal limitations on the accuracy and efficiency of resource purification tasks which apply to any well-behaved resource theory, for both state (static) and channel (dynamical) resources. The general results bring new insights and imply various forms of fundamental limits to a broad range of problems of great theoretical and practical importance, including magic state distillation and fault tolerant quantum computing, quantum error correction, quantum Shannon theory, and quantum circuit synthesis.